Question

Two cells, each of e.m.f. $E$ and internal resistance $r$, are connected in parallel across a resistor $R$ as shown in the figure. The power dissipated through the resistor $R$ is maximum if :

• A. $R=r$
• B. $R=2r$
• C. $R=\frac{3r}{2}$
  
• D. $R=\frac{r}{2}$
  

Answer 1

The correct option is D $R=\frac{r}{2}$



In the figure shown, the power transferred to the resistor $R$ will be maximum when $R$ will be equal to the internal resistance as observed across the terminals connecting $R$

Open-circuit the $R$ terminals, and deactivate the battery(by short-circuiting) the battery terminals .
Then, two internal resistances are in parallel combination.

$R_{eq}=\frac{r}{2}$

Hence, For maximum power to be transfered, $R=\frac{r}{2}$